One has not any conventional energy-momentum conservation law in Lagrangian field theory, but relations involving different stress-energy-momentum tensors associated with different connections. It is not obvious how to choose the true energy-momentum tensor. This problem is solved in the framework of the multimomentum …
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48 results for “Momentum Constraint”
The conformal method is a technique for finding Cauchy data in general relativity solving the Einstein constraint equations, and its parameters include a conformal class, a conformal momentum (as measured by a densitized lapse), and a mean curvature. Although the conformal method is successful in generating constant me…
We study mechanical systems subject to constraint functions that can be dependent at some points and independent at the rest. Such systems are modelled by means of generalized codistributions. We discuss how the constraint force can transmit an impulse to the motion at the points of dependence and derive an explicit fo…
The paper proves positive energy-momentum theorems for charged AdS initial data sets.
problem Proving positive energy-momentum theorems for charged asymptotically AdS initial data sets.
method Introducing a charged energy-momentum functional and establishing positive theorems under a dominant energy condition.
result The charged energy-momentum functional is non-negative on a natural real cone.
Study of closed trajectories in hyperbolic plane with specific curvature constraints.
problem Critical trajectories in hyperbolic plane for a specific energy function.
method Classification of critical trajectories based on momentum causal character, proof of existence of closed trajectories.
result Existence of countably many closed trajectories with time-like momentum.
A new optimizer preserves orthogonality constraints on matrices efficiently.
problem Optimization on Stiefel manifold with orthogonality constraints.
method Interplay between continuous and discrete dynamics leading to a gradient-based optimizer with momentum.
result The method optimizes matrices on Stiefel manifold efficiently and accurately.
In this paper, we propose a geometric integrator for nonholonomic mechanical systems. It can be applied to discrete Lagrangian systems specified through a discrete Lagrangian defined on QxQ, where Q is the configuration manifold, and a (generally nonintegrable) distribution in TQ. In the proposed method, a discretizati…
Momentum accelerates Frank Wolfe algorithms on certain problems.
problem Improving convergence rate of Frank Wolfe algorithms.
method Introducing momentum into Frank Wolfe algorithms and proving faster convergence rate.
result Accelerated Frank Wolfe (AFW) converges with a faster rate of .
We construct solutions with prescribed asymptotics to the Einstein constraint equations using a cut-off technique. Moreover, we give various examples of vacuum asymptotically flat manifolds whose center of mass and angular momentum are ill-defined.
Momentum SGD fails to track nonstationary optima due to drift amplification.
problem Tracking nonstationary optima in stochastic optimization.
method Theoretical analysis of SGD and momentum variants under strong convexity and smoothness.
result Momentum incurs a drift-amplification penalty that diverges as the momentum parameter approaches 1, leading to systematic lag.
Two major momentum-based techniques that have achieved tremendous success in optimization are Polyak's heavy ball method and Nesterov's accelerated gradient. A crucial step in all momentum-based methods is the choice of the momentum parameter which is always suggested to be set to less than . Although the choice…
We show that it is possible to perturb arbitrary vacuum asymptotically flat spacetimes to new ones having exactly the same energy and linear momentum, but with center of mass and angular momentum equal to any preassigned values measured with respect to a fixed affine frame at infinity. This is in contrast to the axisym…
We study --both in theory and practice-- the use of momentum motions in classic iterative hard thresholding (IHT) methods. By simply modifying plain IHT, we investigate its convergence behavior on convex optimization criteria with non-convex constraints, under standard assumptions. In diverse scenaria, we observe that …
New methods reduce constraint violations to certainty in stochastic optimization.
problem Finding a point with certain constraint satisfaction and near-stationarity.
method Single-loop variance-reduced stochastic first-order methods with truncated momentum schemes.
result Achieves strong convergence guarantees for -stochastic stationary points with certain constraint satisfaction.
ChatGPT improves momentum strategies by analyzing news data.
problem Improving risk-adjusted returns in systematic investing.
method Combining LLMs with daily equity returns and news data to predict stock momentum.
result LLM-enhanced momentum strategies outperform benchmarks in Sharpe and Sortino ratios.
In this paper, we proved the mass angular momentum inequality\cite{D1}\cite{ChrusLiWe}\cite{SZ} for axisymmetric, asymptotically flat, vacuum constraint data sets with small trace. Given an initial data set with small trace, we construct a boost evolution spacetime of the Einstein vacuum equations as \cite{ChOM}. Then …
This work removes logarithmic singularities from hyperboloidal initial data without creating new ones.
problem Logarithmic singularities in hyperboloidal initial data sets.
method Evolutionary framework of the constraint equations and generalization of Beyer and Ritchie's result.
result Generic solutions of the constraint equations are free of logarithmic singularities.
The eigenvalue problem for the Sen--Witten operator on closed spacelike hypersurfaces is investigated. The (square of its) eigenvalues are shown to be given exactly by the 3-surface integral appearing in the expression of the total energy-momentum of the matter+gravity systems in Witten's energy positivity proof. A sha…
Proof of local well-posedness for a specific boundary condition in general relativity.
problem Initial boundary value problem in general relativity with umbilic boundary condition.
method Wave coordinates and key observation of momentum constraint validity for umbilic boundaries.
result Local well-posedness established for the initial boundary value problem.
Proves critical points of ADM mass correspond to specific initial data sets.
problem Finding initial data sets with fixed Bartnik boundary data.
method Proves existence of critical points on a Banach manifold.
result Critical points of ADM mass correspond to initial data sets with generalized Killing vector fields.
Paper extends Noether's Theorem to nonholonomic systems, proving conserved momentum.
problem Link between symmetries and first integrals broken in nonholonomic systems.
method Constructive method proving conserved momentum under certain conditions.
result Conserved momentum map in nonholonomic systems, extending Noether's Theorem.
In the first half of this article, we survey the new quasi-local and total angular momentum and center of mass defined in [9] and summarize the important properties of these definitions. To compute these conserved quantities involves solving a nonlinear PDE system (the optimal isometric embedding equation), which is ra…
Generalizes sigma model with Lie algebroid structure and geometric conditions.
problem Consistency of constraints and gauge symmetry in topological sigma models.
method Analysis of geometric conditions and constraints in Hamiltonian and Lagrangian formalisms.
result Identifies universal compatibility condition between Lie algebroid and multi-symplectic structure.
We consider Noether symmetries of the equations defined by the sections of characteristic line bundles of nondegenerate 1-forms and of the associated perturbed systems. It appears that this framework can be used for time-dependent systems with constraints and nonconservative forces, allowing a quite simple and transpar…
New algorithm solves minimax games with linear constraints.
problem Nonconvex minimax games with coupled linear constraints.
method Primal-dual alternating proximal gradient (PDAPG) algorithm.
result Achieves ε-stationary solution within O(ε^(-2)) iterations for strongly concave settings.
This work addresses the instability in asynchronous data parallel optimization. It does so by introducing a novel distributed optimizer which is able to efficiently optimize a centralized model under communication constraints. The optimizer achieves this by pushing a normalized sequence of first-order gradients to a pa…
We develop a projected Nesterov's proximal-gradient (PNPG) approach for sparse signal reconstruction that combines adaptive step size with Nesterov's momentum acceleration. The objective function that we wish to minimize is the sum of a convex differentiable data-fidelity (negative log-likelihood (NLL)) term and a conv…
Unified method for constructing non-vacuum initial data sets in general relativity.
problem Constructing solutions of Einstein constraint equations with coupled matter sources.
method Phase space representation and scaling of matter fields.
result Semi-decoupling of conformal constraint equations for constant-mean curvature initial data.
The study finds that factor momentum is significant only at short lags compared to stock momentum.
problem Investigating the relationship between factor momentum and stock momentum.
method Replicated earlier findings and conducted a spanning test controlling for stock momentum and factor exposure.
result Factor momentum is significant only at short lags after controlling for stock momentum and factor exposure.
SFAG generates realistic financial data that passes trading tests.
problem Financial generative models often produce unrealistic and unstable trading outcomes.
method Introduces SFAG, a GAN variant that aligns stylized facts and optimizes with adversarial loss.
result SFAG generates synthetic data that preserves stylized facts and supports robust trading strategies.
We test the price momentum effect in the Korean stock markets under the momentum universe shrinkage to subuniverses of the KOSPI 200. Performance of the momentum strategy is not homogeneous with respect to change of the momentum universe. It is found that some submarkets generate the higher momentum returns than other …
Introduces homotopy momentum sections on multisymplectic manifolds.
problem No specific problem stated; focuses on introducing a new concept.
method Introduces a new concept of homotopy momentum sections on multisymplectic manifolds.
result Shows that a gauged nonlinear sigma model with Wess-Zumino term has homotopy momentum section structure.
Customer Momentumq-fin.PR
Customer momentum is a positive relationship between a firm's returns and past returns of its customers.
problem Understanding the relationship between a firm's returns and its customers' past returns.
method Examined customer momentum using a long-short equally-weighted decile portfolio and Fama-French factor models.
result Customer momentum generates significant monthly returns and is statistically significant.
This paper examines momentum spillover across multiple asset classes using only pricing data.
problem Challenges in studying momentum spillover across diverse asset classes due to lack of common characteristics.
method Utilised a linear and interpretable graph learning model to reveal momentum spillover network.
result Network momentum strategy yields a Sharpe ratio of 1.5 and an annual return of 22%.
The paper analyzes how hyperparameters affect SGD with momentum's convergence rate.
problem The role of hyperparameters in SGD with momentum's convergence rate.
method Theoretical analysis using a hyperparameters-dependent stochastic differential equation (hp-dependent SDE).
result The optimal linear rate of convergence depends on both the learning rate and the momentum coefficient.
This paper presents generalized momentum mappings for covariant Hamiltonian field theories. The new momentum mappings arise from a generalization of symplectic geometry to , the bundle of vertically adapted linear frames over the bundle of field configurations . Specifically, the generalized field momentum obs…
Hamiltonian Lie algebroidsmath.SG
In previous work with M.C. Fernandes, we found a Lie algebroid symmetry for the Einstein evolution equations of general relativity. The present work was motivated by the effort to explain the coisotropic structure of the constraint subset for the initial value problem by extending the notion of hamiltonian structure fr…
We give a detailed discussion about existence and uniqueness of Lu's momentum map. More precisely, we introduce the infinitesimal momentum map, and we study its properties. This allows us to describe the theory of reconstruction of the momentum map from the infinitesimal one. We provide the conditions for the uniquenes…
Momentum ResNets improve ResNets' memory efficiency.
problem Memory inefficiency in deep residual neural networks (ResNets).
method Adding a momentum term to the forward rule of ResNets to make them invertible.
result Momentum ResNets can learn any linear mapping up to a multiplicative factor, improving memory efficiency.
We introduce various quantitative and mathematical definitions for price momentum of financial instruments. The price momentum is quantified with velocity and mass concepts originated from the momentum in physics. By using the physical momentum of price as a selection criterion, the weekly contrarian strategies are imp…
Application of Langevin Dynamics to Advance the Quantum Natural Gradient Optimization Algorithmquant-ph
New algorithm Momentum-QNG improves optimization of quantum circuits.
problem Optimizing variational quantum circuits to avoid local minima.
method Applied Langevin dynamics to QNG, introducing momentum term.
result Momentum-QNG outperforms basic QNG and other optimizers.
We demonstrate the possibility of what we call sparse learning: accelerated training of deep neural networks that maintain sparse weights throughout training while achieving dense performance levels. We accomplish this by developing sparse momentum, an algorithm which uses exponentially smoothed gradients (momentum) to…
Momentum speeds up evolutionary processes in machine learning.
problem Accelerating convergence in evolutionary dynamics.
method Combining momentum from machine learning with evolutionary dynamics using information divergences as Lyapunov functions.
result Momentum accelerates convergence of evolutionary dynamics, including the replicator equation and Euclidean gradient descent.
Structural Limits of OHLCV-Based Intraday Signals in MNQ Futures: A Systematic Falsification Studyq-fin.TR
Study finds no statistically significant trading edge in MNQ futures signals from OHLCV data.
problem Testing intraday momentum signals from OHLCV data in MNQ futures under realistic execution constraints.
method 947 trading days of five-minute data, 14 signal families evaluated, strict institutional criteria applied.
result No signal satisfies all criteria simultaneously, gross edge insufficient to overcome costs.
Contact manifolds' momentum polytopes are convex.
problem Understanding the structure of contact manifolds.
method Using isomorphism to toric varieties.
result Momentum polytopes of contact manifolds are convex.
Strictly enforcing orthonormality constraints on parameter matrices has been shown advantageous in deep learning. This amounts to Riemannian optimization on the Stiefel manifold, which, however, is computationally expensive. To address this challenge, we present two main contributions: (1) A new efficient retraction ma…
Unified model learns from both time-series and cross-sectional momentum features.
problem Separate time-series and cross-sectional momentum strategies do not consider concurrent relationships.
method Spatio-Temporal Momentum strategies using neural networks to combine both types of momentum.
result Simple neural network with single fully connected layer generates trading signals for all assets.
SMG combines shuffling and momentum for non-convex optimization.
problem Non-convex finite-sum optimization problems.
method Shuffling Gradient-based method with momentum.
result Established state-of-the-art convergence rates for SMG.